added iterative solution for product sum problem

Signed-off-by: negi153 <mukesh7758negi@gmail.com>

Author: negi153

data_structures/arrays/product_sum.py

@@ -92,6 +92,78 @@ def product_sum_array(array: list[int | list]) -> int:
     return product_sum(array, 1)
 
 
+def product_sum_iterative(arr: list[int | list | set | tuple]) -> int:
+    """
+    Calculates the product sum of an array using iterative approach.
+
+    Logic :
+        1. Loop until input list have nested list/tuple/set
+            1. iterate on each item in input array
+            2. if item is nested list/tuple/set then
+                - multiply the nested item with it's depth and add it's elements
+                  to new array
+            3. if item is not nested then
+                add item to total sum
+            4. update old array with new array and increment depth value
+
+    Algorithm flow example ->
+        Step 1 --> Array - [5, 2, [-7, 1], 3, [6, [-13, 8], 4]]
+                   total sum = 0 + () = 0
+        Step 2 --> Array - [-7, 1, -7, 1, 6, [-13, 8], 4, 6, [-13, 8], 4]
+                   total sum = 0 + (5 + 2 + 3) = 10
+        Step 3 --> Array - [-13, 8, -13, 8, -13, 8, -13, 8, -13, 8, -13, 8]
+                   total sum = 10 + (-7 + 1 -7 + 1 + 6 + 4 + 6 + 4) = 18
+        Step 4 --> Array - [-13, 8, -13, 8, -13, 8, -13, 8, -13, 8, -13, 8]
+                   total sum=18 +(-13 + 8 -13 + 8 -13 + 8 -13 + 8 -13 + 8 -13 + 8)= -12
+
+    Args:
+        array(List[Union[int, List, Set, Tuple]]): The array of integers/lists/tuple/set
+
+    Returns:
+        int: The product sum of the array.
+
+    Examples:
+        >>> product_sum_iterative([1, 2, 3])
+        6
+        >>> product_sum_iterative([1, [2, 3]])
+        11
+        >>> product_sum_iterative([1, [2, [3, 4]]])
+        47
+        >>> product_sum_iterative([0])
+        0
+        >>> product_sum_iterative([-3.5, [1, [0.5]]])
+        1.5
+        >>> product_sum_iterative([1, -2])
+        -1
+
+    """
+
+    # depth of the nested list/tuple/set
+    next_depth = 2
+
+    # flag to check whether list has nested items or not
+    nested_list_check = True
+
+    total_sum = 0
+
+    while nested_list_check:
+        # list to store new items
+        new_arr = []
+        nested_list_check = False
+
+        for item in arr:
+            if isinstance(item, list | tuple | set):
+                new_arr.extend(list(item) * next_depth)
+                nested_list_check = True
+            else:
+                total_sum += item
+
+        arr = new_arr
+        next_depth += 1
+
+    return total_sum
+
+
 if __name__ == "__main__":
     import doctest